"On Smoothness of the Green Function"




Alexander Goncharov



Abstract: If a compact set K is regular with respect to the Dirichlet problem, then the Green function g of the complement of K with pole at infinity is continuous throughout the complex plane. We discuss character of continuity of g near the boundary of the domain, review new results by Totik and Andrievskii concerning compact sets with optimal smoothness of g and describe the smoothness of the Green functions for the complement of rarefied Cantor-type sets in terms of the function that gives the logarithmic measure of sets. Markov's constants of the corresponding sets are evaluated. The result is joint with M.Altun.











Tea and cookies will be served before the seminar.



Date:  Wednesday, April 22, 2009

Time: 14.40

Place: Mathematics Seminar Room, SA-141